Melt the butter in a small saucepan over low heat.
Add the cocoa powder to the melted butter and stir until smooth.
Transfer the cocoa and butter mixture to a medium mixing bowl.
Sift 2 1/2 cups of the powdered sugar.
With an electric mixer on low speed, beat in about 1 1/4 cups of the powdered sugar along with 3 tablespoons of the milk. Beat in another 1 1/4 cups of powdered sugar and 2 tablespoons of milk. Add more milk or powdered sugar if needed for consistency.
The recipe makes enough to frost arectangular 1-layer or 2-layer cake.